Calculating how fast distance changes between ships

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SUMMARY

The problem involves calculating the rate of change of distance between two ships, A and B, at 4:00 PM. Ship A starts 50 km west of Ship B and sails south at 30 km/h, while Ship B sails north at 20 km/h. After 4 hours, Ship A travels 120 km south, and Ship B travels 80 km north, resulting in a total separation of 200 km north/south and an initial 50 km east/west separation. The distance between the ships can be calculated using the Pythagorean theorem, incorporating both components of their movement.

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Homework Statement



At noon, ship A is 50km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 20km/h. How fast is the distance between the ships changing at 4:00pm in km/h.

Homework Equations





The Attempt at a Solution



http://img822.imageshack.us/img822/2420/shipq2.png

but the final answer is coming out wrong
 
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I don't understand the very first line of your answer. Why are you taking the squares of the velocities? Where is the 50km in this? If you substitute t = 0 in your equation, what number should you get?
 
Ship A is heading south at 30 for 4 hours so travels 120 km. Similarly B travels 80 due north.
So they become separated by 200km north/south.
They are separated by 50 km due east west to begin with.

So the distance between the ships is? (pythagoras).
The angle of the same triangle is also the direction cosine of the motion so you can use that to calculate their mutual speed.
 

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